The population of a town increases every year by [tex]$10\%$[/tex]. At the end of two years, the total population of the town was 30,000. If it includes 5,800 people who were added by migration,
(a) If the initial population is [tex]$P$[/tex] and the population after [tex]$T$[/tex] years is [tex]$P_T$[/tex], write the formula to calculate [tex]$P_T$[/tex].
[tex]\[ P_T = P \left(1 + \frac{R}{100}\right)^T \][/tex]
(b) Write the population after 2 years.
[tex]\[ P_T = 30,000 \][/tex]
(c) Find the population before 2 years.
[tex]\[ P = \frac{P_T - 5800}{\left(1 + \frac{R}{100}\right)^2} \][/tex]
[tex]\[ P = \frac{30,000 - 5,800}{(1.10)^2} \][/tex]
[tex]\[ P \approx 20,000 \][/tex]
(Note: Removed irrelevant part about "simple population growth in four years" as it doesn't fit the context of the task given.)